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半喂入式花生摘果機設(shè)計【全套含CAD圖紙、說明書】,全套含CAD圖紙、說明書,半喂入式,花生,摘果機,設(shè)計,全套,cad,圖紙,說明書,仿單 附錄 英文資料翻譯 一個接口安裝有限元的水平集方法算法，實施，分析和應(yīng)用 1.1移動界面及其數(shù)學(xué)說明 移動界面是不同媒介之間分隔的界限，它們一般發(fā)生在科學(xué)工程領(lǐng)域和日常生活中，例如冰和水的邊界溫度變化 、水包油泡沫動作的邊界移動，更多的例子包括晶體生長表面、相固固相變的界限、網(wǎng)站接口區(qū)域界限、以及區(qū)分不同部位的材料界線等。晶界在多晶體、鐵磁材料的磁疇壁中、兩相流體流量、以及在液態(tài)運動時大生物分子表面生成。 在這里，在廣義上可以理解為：一個接口可以是一個幾何面有沒有厚度或者尖接口，它也可以指一個分散接口，可以有一定的厚度，如幾個原子的直徑。相比與那些固定接觸點，移動接處點的屬性越來越重要，作為尺度越來越小。隨著現(xiàn)代技術(shù)的需求，大量的設(shè)備在規(guī)模要小得多，在移動界面的研究變得越來越重要。 一個移動的接處點可以通過一個精確的數(shù)學(xué)數(shù)據(jù)描述接口，也就是說，一個沒有任何厚度的表面，或通過場函數(shù)的描述，不斷在不同區(qū)域的值與突出的區(qū)域在一個區(qū)間連續(xù)過渡。后者代表一個接口。后者通常被稱為擴散描述接口描述。在這篇論文中，我們會研究大幅接口描述移動接口。 研究一個移動的接口，有如下方程： V(t) =dx(t)dt 這樣一個點的速度（矢量）定義為該接觸點的公式，然后由正常的速度（正常的COM分量速度矢量在每個接口點）方程式去表述，正常的速度通常被稱為移動界面運動規(guī)律。因此，就可以在數(shù)學(xué)上確定移動界面某些運動規(guī)律管接口的正常速度。 在一般情況下，運動規(guī)律，從基礎(chǔ)物理、化學(xué)等中得到。如果我們用??=（t）來定義，就可以得到運動規(guī)律 Vn = ?H,其中Vn= Vn的（的x，t）表示正常速度（即正常分量速度矢量）的點x在時間t∈??中的平均曲率。在許多應(yīng)用中，還涉及到更通常速度的物理量。因此，偏微分方程（PDE）通常必須滿足其中一項某些數(shù)量的接觸點的描述作用，如溫度場。在這種情況下，通過接觸點介紹運動關(guān)系公式里的接口一側(cè)偏微分方程的解。作為接口不斷發(fā)展了偏微分方程必須在不斷發(fā)展的領(lǐng)域解決。該接觸點可能是一個復(fù)雜的形狀，比如能隨時間變化合并或分裂的拓撲結(jié)構(gòu)。計算科學(xué)家面臨的挑戰(zhàn)就是準(zhǔn)確地解決這些問題。 圖1.1：與邊界?典型域。界面顯示分離??地區(qū) -和+。 1.2.1標(biāo)記方法 該標(biāo)記方法是一種離散拉格朗日方法，在一個接觸面上設(shè)點的集合。在二維空間的點連鎖與線段在一起，形成一條曲線。在移動界面上，這些標(biāo)記每個點的速度是在每一個時刻決定的，然后該點在時間上向前移動少量（見圖1.2），這種方法的缺點是難以拓撲變化處理，另一個缺點是接觸面的定位精度取決于密切標(biāo)記粒子沿界面的地方。隨著時間的推移，某些指標(biāo)可能會移動生成到了更遠的分界面位置附近的更多的錯誤（見圖1.3）。因此，任何算法需要定期檢查安置粒子以確保他們足夠接近以達到預(yù)期準(zhǔn)確性。此外，如果有太多并攏沿界面，某些標(biāo)記顆粒可能需要被刪除或重新分配。另一個有缺點的標(biāo)記的方法是，它可以成為基于曲率運動不穩(wěn)定的接口，界面的曲率計算的小錯誤將增長時間。圖1.2：標(biāo)記方法的說明。 （一）標(biāo)記（點）代表界面位置。 （二）在每一個時刻每個標(biāo)記在其指定的移動速度到新的位置。 （三）在其新的位置接口。 1.2.2固體單元的流體方法 與此相反的標(biāo)記方法，固體單元的流體的方法跟蹤接口有內(nèi)在的聯(lián)系。它使用計算域的單元格網(wǎng)格，每個單元格中包含一個介于0和1的值。 圖1.3：一個標(biāo)記方法的缺點。 （一）兩個接口接近對方。 （二）標(biāo)記需要刪除后接口重疊。 該接口單元經(jīng)過包含一個值介于0和1的接口在某處經(jīng)過該單元格。該接口的位置可以被近似為基礎(chǔ)在單元格中的值，但是許多較小的單元可能需要得到想要的精度（見圖1.4）。如正常量的方向和曲率該接口是很難用這種方法計算準(zhǔn)確。盡管有這樣的缺點，但是這種方法已經(jīng)成功的被用來模擬移動界面，特別是傳播火焰的界面描述。 圖1.4：固體體積的流體方法的說明。 （一）接口圍陰影區(qū)。 （二）網(wǎng)格單元格的值由陰影填充單元比例計算地區(qū)。 1.2.3水平集方法 水平集方法，首先在[OS88]介紹的是一個通過歐拉方法含蓄地描述了接口。這種方法的出發(fā)點是為了說明一個移動的表面在t時刻，作為一個輔助集的零水平含蓄函數(shù)φ=φ（的x，t）。例如，如果是三維表面在任何時間t（如球體），那么該函數(shù)φ（x，t）是一個函數(shù)的三維空間，即x的定義有三個坐標(biāo)。 為方便起見，我們可以假設(shè)函數(shù)正面的有效數(shù)字在一側(cè)的接口以及對方負值。我們稱φ為一級別設(shè)置功能。很明顯，這些功能有很大的不確定。水平集功能的進化，其零水平集始終代表了這樣一種方式時間接口的位置。對已知的水平集方法的優(yōu)勢之一是使它進行移動接口拓撲變化（見圖1.5）。 水平集函數(shù)的演化是由底層運動規(guī)律的運動界面正常速度生成，如果水平設(shè)置功能是表示一個點上的X接口和時間t為φ=φ，則方程確定水平集函數(shù)為?tφ+ Vn的|?φ|=0。其中?t表示時間導(dǎo)數(shù)和梯度?表示空間。這方程被稱為水平集方程。一個人需要延長正常速度提示（通常只在接口上確定）遠離接口，這樣的水平集方程可以解決一個適當(dāng)?shù)目臻g域。 推導(dǎo)水平集方程和水平集方法的詳細資料載于第2章。 圖1.5：一個例子集函數(shù)的水平隨著時間的推移（左欄）擬訂與零的水平代表著該接口（右相應(yīng)地塊列）。 1.3本論文的主要貢獻 在這篇論文中的項目，我們開發(fā)了一個新的水平集方法。這是一接口安裝有限元的水平集方法。對這種情況的主要特點方法是：網(wǎng)格：我們使用格點與頂點在一個統(tǒng)一的基礎(chǔ)網(wǎng)格。在每個時間步長的網(wǎng)格細化到產(chǎn)品的接口貼網(wǎng)而前plicitly定位運動界面。雖然它需要額外的時間來完善在每個時間步長網(wǎng)，某些計算變得更加容易。重新初始化的新方法：我們重新初始化水平集函數(shù)求解泊松方程類型的問題。我們保持平穩(wěn)的水平集函數(shù)通過實施跨梯度跳轉(zhuǎn)條件界面，然后有最小二乘法解決一超定系統(tǒng)。這種方法產(chǎn)生一個新的水平集函數(shù)、平穩(wěn)區(qū)域和整個接口，平穩(wěn)過渡非常重要，因為它增加了準(zhǔn)確性曲率計算，詮釋了一些例子來演示如何重新初始化工作。 新方法的速度擴展：水平集方法有賴于速度函數(shù)附近的接口定義，不只是在接口處，因此，如果接口的速度只在接口上已知時，我們需要擴大這一速度遠離流暢的界面。我們解決拉普拉斯的內(nèi)部和外部的接口上使用方程速度接口作為邊界條件，這是一個簡單的方式來擴展速度。如果需要，我們可以平滑施加梯度跳到對面的條件接口和解決最小二乘。 （這類似于我們的重新初始化方法。） 曲率近似數(shù)值??分析：我們也提出了一種新方法計算出的水平集函數(shù)的曲率。這相當(dāng)于美國荷蘭國際標(biāo)準(zhǔn)中有限先和二階導(dǎo)數(shù)差逼近，但這種方法可能在某些應(yīng)用中比較簡單，因為過程中的其他步驟該算法在計算中使用的數(shù)量可能被重復(fù)使用。一個證明和這一計算的準(zhǔn)確性例子可以給出。凝固問題上的應(yīng)用：在這里，我們證明了算法用它來解決Stefan問題。樹突狀凝固模型的例子，一個凍結(jié)物塊放入冷液體中。包括的影響有各向同性、各向異性，不過沒有表面張力為藍本，其他的例子顯示了不同的表面張力各向異性的相位角的影響。 這些例子表明，如果沒有那些接口配件時，用我們的方法產(chǎn)生了此前由一個嚴格的有限差分格式制作的類似的效果。應(yīng)用分子溶劑：在這里，我們證明了算法用它來尋找最佳的溶劑系統(tǒng)溶質(zhì)溶劑接觸面。我們使用平衡溶劑化系統(tǒng)變分隱式溶劑模型非極性分子，每個分子由一組特定的原子在計算上組成。初始界面是封閉的原子移動的方向，減少了自由能。包括空閑的能源對溶質(zhì)和溶質(zhì)溶劑型接口的范德華能源相互作用。我們的例子演示了我們的方法如何收集最佳溶質(zhì)溶劑溶劑化系統(tǒng)的各種接觸面。 附錄 英文資料翻譯 1.1 MovAn interface-fitted finite element based level set method Algorithm, implementation, analysis and applicationsing Descriptions Moving interfaces are boundaries that separate different media that are deforming or flowing. They occur commonly in science, engineering and daily life. For instance, an ice-water boundary moves during the change of temperature and an oil bubble moves in water. More examples include growing crystal surfaces, phase boundaries in solid-solid phase transformations such as precipitate and martensite interfaces,domain boundaries that separate different parts of material such as grain boundaries in polycrystals, domain walls in ferromagnetic materials, two phase fluid flows, and surfaces of large biomolecules moving in water. Here interfaces are understood in a broad sense: an interface can be a geometrical surface that has no thickness—a sharp interface; it can also mean a diffuse interface that can have certain thickness, e.g., of a few atomic diameters. Compared with those of bulk phases, the properties of moving interfaces can be more and more important as the length scales become smaller and smaller. As modern technologies demand heavily that devices be much smaller in scale, the study of moving interfaces has become more and more important. A moving interface can be mathematically described by a sharp interface, a surface without any thickness, or by a field function that takes constant values in different regions with a sharp but continuous transition from one region to another, representing an interface. The latter description is often called diffused interface description. In this thesis, we will consider a sharp interface description of moving interfaces. Consider a moving interface which is represented by the set of points ?? =(t) which depends on time t. Let x(t) be an arbitrary point that remains on ??. The velocity (vector) of such a point is defined by V(t) =dx(t)dt. (1.1.1) The interface motion is then determined by the normal velocity (the normal com-ponent of the velocity vector) at each point of the interface. Equations that determine the normal velocities are often called motion laws for moving interfaces. Thus, moving interfaces are mathematically determined by certain motion laws governing the normal velocity of the interface. In general, motion laws are given from the underlying physics, chemistry, etc. Motion by mean curvature is a com-mon and important example of such motion laws. If we denote by ?? = (t) the geometrical surface at time t, then the motion law is Vn = ?H, where Vn = Vn(x, t) denotes the normal velocity (the normal component of the velocity vector) of the point x ∈ ?? at time t, and H is the mean curvature. In many applications, normal velocity also involves more physical quantities.Therefore partial differential equations (PDEs) typically must be satisfied on either side of the interface for certain quantities such as the temperature field. In such a case, the movement of the interface is then described in terms of the relationship between the solutions of the PDEs on either side of the interface. As the interface continually evolves the PDEs must be solved on continually evolving domains. The interface may be a complex shape and can change topologically over time by merging or breaking apart. The challenge for computational scientists is to accurately solve such problems. 1.2 Different Types of Numerical Methods for Interface Motion Let us imagine two regions separated by an interface that is moving in time according to a certain motion law. In two dimensions the interface would be a curve separating two areas. In three dimensions the interface would be a surface separating two volumes. We would like to track this moving interface numerically. We can designate an interior region and exterior region and call them ? and +. The interface separating ? and + is designated by ??, and the boundary of the computational domain is designated by ? (see Figure 1.1). Figure 1.1: A typical domain with boundary ?. Interface ?? shown separating regions ? and +. 1.2.1 Marker Method The marker method is a Lagrangian method that discretizes the interface with a set of points located on the interface. In two dimensions the points are chained together with line segments to form a curve. To move the interface, at each of these marker points the velocity is determined at each time step. The points are then moved forward in time a small amount (see Figure 1.2). One drawback of this method is that topological changes are difficult to handle. A sophisticated method must therefore be employed to check if two regions of ? join together or if one region splits into two. Another drawback is that the accuracy of the location of the interface depends on how closely the marker particles are place along the interface. As time progresses, some markers may move farther apart creating more error in the location of the interface near those points (see Figure 1.3). So any algorithm needs to periodically check the placement of the particles to insure that they are sufficiently close together to have the desired accuracy. Also, some marker particles may need to be removed or redistributed if there are too many close together along the interface. Yet another drawback of the marker method is that it can become unstable with curvature based motion of the interface. Small errors in the calculated curvature of the interface will grow in time. (c) Figure 1.2: Illustration of the marker method. (a) Markers (dots) represent the interface location. (b) At each time step each marker is moved at its specified velocity to its new location. (c) Interface in its new location. 1.2.2 Volume-of-Fluid Method In contrast to the marker method, the volume-of-fluid method tracks the interface implicitly. It uses a grid of cells on the computational domain, and each cell contains a value between 0 and 1. Cells completely contained in ? have a value Figure 1.3: One drawback of the marker method. (a) Two interfaces approaching each other. (b) Markers need to be removed after interfaces overlap. of 1 and those completely contained in + have value 0. Cells that the interface passes through contain a value between 0 and 1 based on where the interface passes through that cell. The interface location can then be approximated based on the values in the cells, but many smaller cells may be required to get a desired accuracy (see Figure 1.4). Quantities such as the normal direction and curvature of the interface are difficult to calculate accurately with this method. In spite of the drawbacks, this method has been used to model moving interfaces successfully,in particular, flame front propagation [Cho80, Set84]. Figure 1.4: Illustration of the volume-of-fluid method. (a) Interfaces enclosing shaded areas. (b) Grid cell values based on proportion of cell filled by shaded areas. 1.2.3 Level Set Method The level set method, first introduced in [OS88] is an Eulerian method that describes the interface implicitly. The starting point of this method is to describe a moving surface ?? = (t) at time t implicitly as the zero level set of an auxiliary function φ = φ(x, t), i.e., (t) = {x : φ(x, t) = 0}. For instance, if ?? is a three-dimensional surface (such as a sphere) then the function φ(x, t) at any time t is a function defined on the three-dimensional space, i.e., x has three coordinates. For convenience, we can assume that the function takes on positive values on one side of the interface and negative values on the other side. We shall call φ a level set function of ??. Clearly such functions are vastly nonunique. The level set function evolves over time in such a way that its zero level set always represents the location of the interface. One of the known advantages of the level set method is that it captures naturally, and easily, topological changes of moving interfaces(see Figure 1.5). The evolution of the level set function is determined by the underlying motion law governing the normal velocity Vn of the moving interface. If the level set function is denoted by φ = φ(x, t) for a point x on the interface and time t, then the equation determining the level set function is given by ?tφ + Vn|?φ| = 0. where ?t denotes the time derivative and ? denotes the spatial gradient. This equation is called the level set equation. One needs to extend the normal velocity Vn (usually determined only on the interface) away from the interface so that the level set equation can be solved in an appropriate space domain. The derivation of the level set equation and more details of the level set method are given in Chapter 2.